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Finding the Third Proportional to 415,461 and 678,345

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Solution

The third proportional to 415,461 and 678,345 is: 1,107,569.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    415,461 : 678,345 = 678,345 : x
  2. Step 2: Convert to fraction form
    415,461/678,345 = 678,345/x
  3. Step 3: Cross multiply
    415,461x = 678,345 × 678,345
  4. Step 4: Simplify right side
    415,461x = 460,151,939,025
  5. Step 5: Solve for x
    x = 460,151,939,025/415,461
  6. Step 6: Final answer
    x = 1,107,569.52

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.